Description:

Department of Statistics 2021-2022 Seminar Series (joint with Biostatistics) - Fall 2021

“Additive Models for Density Responses in Functional Data Analysis”

Kyunghee Han, Assistant Professor, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

Abstract:

Data in the form of samples of densities or distributions are increasingly encountered in statistical analysis and there is a need for flexible regression models that accommodate random densities as responses. Such models are of special interest for multivariate continuous predictors, where unrestricted nonparametric regression approaches are subject to the curse of dimensionality. In this talk, a transformation approach to functional additive models will be presented, where the responses are random distributions and multiple predictors are coupled with responses. To overcome the problem that distributions do not form a vector space, we utilize a class of transformations that map densities to unrestricted square integrable functions and then deploy an additive functional regression model to fit the responses, finally transforming back to density space. We implement the proposed additive model with an extended version of smooth backfitting and establish the consistency of this approach, including rates of convergence. This is joint work with Hans-Georg Muller and Byeong Uk Park.